Calculate number of unique ways to make change with a set of coins

coin_change_solutions.py

def partial_soln(solns, coins, target):
    solns[target] = []
    for i in coins:
        x = target - i
        if x in solns:
            for xx in solns[x]:
                new_item = tuple(sorted(list(xx) + [i]))
                solns[target].append(new_item)

def solution(coins, target):
    solns = {0: [()]}
    for i in range(1, target + 1):
        partial_soln(solns, coins, i)
    return solns[target]

def unique_solution(coins, target):
    s = solution(coins, target_amt)
    solutions = set(s)
    return sorted(solutions)

if __name__ == '__main__':
    # target_amt = 4
    # coins = [1, 2, 3]
    coins = [2, 5, 3, 6]
    target_amt = 10
    print(unique_solution(coins, target_amt))